1. Field of the Disclosure
The present invention relates to a capacitance measuring apparatus and capacitance measuring method that are used for quasi-static capacitance measurement of a capacitance element in the development of semiconductor devices and semiconductor processes.
2. Discussion of the Background Art
The capacitance of a device under test (DUT) is measured as part of the evaluation that is performed in the development of semiconductor devices and semiconductor processes. The capacitance measurement of a device under test generally is a capacitance measurement at high frequency or a capacitance measurement at low frequency (quasi-static capacitance measurement). As a result of semiconductor processes being conducted on micro/nano levels in recent years, the measured capacitance at a low frequency has become smaller, and there is a need for technology with which high-precision measurement is possible.
The step voltage method is a means for measuring the amount of change in the charging charge that is produced when the voltage applied to a device under test is changed, and then finding the capacitance value of the device under test from the amount of change in this charging charge and the amount of change in the applied voltage. JP Unexamined Patent Publication (Kokai) 2002-168,893, for instance, discloses technology relating to the step voltage method.
However, there is a problem with the micro/nano-level processing of semiconductors in that in the case of a capacitance measurement at low frequency in particular, a large leakage current attributed to the resistance component of the device under test flows into the ammeter for measuring the charging current flowing to the device under test, and this leads to errors in the capacitance measurement. FIG. 10 shows an example of the effect of this leakage current. When the voltage applied to the device under test is changed, charging current flows to the device under test and the charging charge changes (surface area of current (I) graph in FIG. 10). If there is no leakage current, the only current flowing into the ammeter will be charging current that is flowing through the device under test, but when leakage current is generated, in addition to the charging current flowing through the device under test, leakage current flows into the ammeter. As a result, it is not possible to correctly measure the amount of change in the charging charge of the device under test. There is therefore a need for a capacitance measuring method with which it is possible to correct for the charge of this leakage current component. The following is a conventional example of a capacitance measuring method with which it is possible to correct for the leakage current component.
The relationship between capacitance C of the device under test (units F), charging charge Q (units C), and applied voltage V (units V) is represented by the following formula:Q=CV   (1)
Assuming that capacitance C of the device under test is constant, when voltage V applied to the device under test is changed from a certain Vset1 to a different voltage Vset2, the charging charge of the DUT also changes from a certain value Q1 to a different value Q2. In essence, the charging charge changes by ΔQ (=Q2−Q1). The amount of change ΔQ in the charging charge is found by the integration of charging current I as shown in the following formula.ΔQ=∫Idt   (2)|
FIG. 11 is a drawing showing an example of a case in which the amount of change ΔQ in the charging charge when applied voltage has been changed is found by a rectangular approximation by period ΔtPLC defined as a predetermined integer multiple of the PLC (power line cycle). When the frequency of the power source voltage is 50 Hz, ΔtPLC is, for instance, 20 ms and when the frequency of the power source voltage is 60 Hz, it is, for instance, 16.67 ms. In this case, the amount of change ΔQ in the charging charge is approximately represented by the following formula:ΔQ≈ΣIk*ΔtPLC   (3)|
where k=1, 2, . . . , Tcinteg/−ΔtPLC. Tcinteg is the integration period of the charging current.
FIG. 14 is a block diagram for measurement by the conventional step voltage method; the output of a variable voltage source 82 is connected to one terminal of a device under test (DUT) 81, and the other end of a device under test 81 is connected to a ground terminal via an ammeter 84. On the other hand, a voltmeter 83 is connected to the output of variable voltage source 82. FIG. 12 is a drawing showing the measurement sequence of the conventional step voltage measurement, and shows the change in the applied voltage of one measurement step. It should be noted that a first measuring unit is used for variable voltage source 82 and voltmeter 83, and a second measuring unit is used for ammeter 84. First, the value of the applied voltage is set at a certain value Vset1 by the first measuring unit. When time delay1, which has been predetermined from the applied voltage setting, has lapsed, applied voltage V1 is measured by the first measuring unit, and then the leakage current IL1 is measured by the second measuring unit, which is an ammeter. The measurement of applied voltage V1 and the measurement of leakage current IL1 are preformed in succession in this way because a single A/D converter is shared by the first measuring unit and the second measuring unit. Once applied voltage V1 has been measured, the measurement of charging current by the second measuring unit is initiated and the applied voltage setting is changed to a different setting Vset2. The applied voltage is thereby increased.
The measurement of the charging current by the second measuring unit involves repeating Tcinteg/ΔtPLC times in ΔtPLC intervals and then finding the integral as the amount of change in the charging charge ΔQtotal. Once measurement of the charging charge is complete, the applied voltage V2 is measured by the voltage source and then the leakage current IL2 is measured by the second measuring unit.
The capacitance value C is found using the following formulas:
                                                        C              =                                                Δ                  ⁢                                                                          ⁢                                      Q                    /                    Δ                                    ⁢                                                                          ⁢                  V                                =                                                      (                                                                  Δ                        ⁢                                                                                                  ⁢                                                  Q                          total                                                                    -                                              Δ                        ⁢                                                                                                  ⁢                                                  Q                          Leak                                                                    +                                              Q                        correction                                                              )                                    /                                      (                                                                  V                        2                                            -                                              V                        1                                                              )                                                                                                                          =                                                {                                                            (                                              Σ                        ⁢                                                                                                  ⁢                                                  I                          k                                                *                        Δ                        ⁢                                                                                                  ⁢                                                  t                          PLC                                                                    )                                        -                                          Δ                      ⁢                                                                                          ⁢                                              Q                        Leak                                                              +                                          Q                      correction                                                        }                                /                                  (                                                            V                      2                                        -                                          V                      1                                                        )                                                                                                                            (              4              )                                                                          (              5              )                                          
Here, ΔQLeak is the amount of change in the charging charge due to leakage current. This is found by the following formula using trapezoid approximation, based on the assumption that the charging charge increases linearly over time as shown in FIG. 13.ΔQLeak=1/2(IL1−IL2)τ+IL2(Tcinteg−τ)   (6)
Here, τ is the time for which the device under test is charged, and this time is determined as described below.
By means of this measurement, the status of the second measuring unit is monitored at the same time that the second measuring unit measures the charging current every ΔtPLC, and if the output voltage and the voltage setting are not the same, the device under test is being charged. Charging is completed at the time when the output voltage and voltage setting become the same (this state is referred to as the Vloop state hereafter).
It should be noted that the charging current is measured every ΔtPLC period and that the status of the second measuring unit is monitored in order to cancel the effect of power line noise.
Qcorrection in formula (4) is the charge that is used to charge to the capacitance connected in parallel to the range resistance inside the second measuring unit.
When the measurement of leakage current IL2 by the second measuring unit is completed, a specific time delay2 is allowed to lapse and then the next step is started, in essence, the voltage setting is raised, and the same measurement is performed.
Nevertheless, by means of the above-mentioned conventional method for measuring capacitance there is a problem in that when the leakage current becomes much larger than the charging current, the leakage current accounts for more of the current flowing through the ammeter than does the charging current, the charging current becomes a small part of the ammeter measuring range, and there is a reduction in the timing range and the S/N (signal-to-noise ratio).